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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Kepler's Laws of Planetary Motion

  • question_answer
    A planet moves around the sun. At a given point P, it is closest from the sun at a distance \[{{d}_{1}}\] and has a speed \[{{v}_{1}}\]. At another point Q,  when  it is farthest from the sun at a distance \[{{d}_{2}}\], its speed will be [MP PMT 1987; DCE 2002]

    A)             \[\frac{d_{1}^{2}{{v}_{1}}}{d_{2}^{2}}\]      

    B)             \[\frac{{{d}_{2}}{{v}_{1}}}{{{d}_{1}}}\]

    C)             \[\frac{{{d}_{1}}{{v}_{1}}}{{{d}_{2}}}\]          

    D)             \[\frac{d_{2}^{2}{{v}_{1}}}{d_{1}^{2}}\]

    Correct Answer: C

    Solution :

                    Angular momentum remains constant             \[m{{v}_{1}}{{d}_{1}}=m{{v}_{2}}{{d}_{2}}\,\Rightarrow \,{{v}_{2}}=\frac{{{v}_{1}}{{d}_{1}}}{{{d}_{2}}}\]


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